12556aca-8d8f-44ef-9988-11abf8621c38.html

<h3>Activity (25 minutes)</h3>
<p>In this activity, students find areas and missing dimensions of rectangles. The dimensions are binomials, and the areas are polynomials. </p>
<p>Students apply their understanding of multiplication, factoring, and division of polynomials to find the missing dimensions and areas of the rectangles.</p>
<h4>Launch</h4>
<ol><li>Arrange students in groups of 2. </li>
  <li>Give students time to complete the table.</li> 
  <li>Follow with a brief whole-class discussion.</li></ol>
<h4>Student Activity</h4>
<p>Use the given information in the table to find the missing length, width, or area of each rectangle. Be prepared to discuss the strategies you used as you found the missing measures.</p>
<table class="os-raise-wideadjustedtable">
  <thead>

    <tr>
      <th scope="col">
        Rectangle
      </th>
      <th scope="col">
        Length (units)
    </th>
      <th scope="col">
        Width (units)
    </th>
      <th scope="col">
        Area (square units)
     </th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>
        A
      </td>
      <td>
        \(x+3\)
      </td>
      <td>
        \(x-4\)
      </td>
      <td></td>
    </tr>
    <tr>
     <td>
        B
      </td>
      <td></td>
      <td>
        \(3x-5\)
      </td>
      <td>
        \(9x^2-25\)
      </td>
    </tr>
    <tr>
      <td>
        C
      </td>
      <td></td>
      <td></td>
      <td>
        \(x^2+8x+16\)
      </td>
    </tr>
    <tr>
      <td>
        D
     </td>
      <td>
        \(x-2\)
      </td>
      <td></td>
      <td>
        \(2x^2-3x-2\)
      </td>
    </tr>
    <tr>
      <td>
        E
     </td>
      <td></td>
      <td>
        \(x+6\)
      </td>
      <td>
        \(x^2+4x-12\)
      </td>
    </tr>
    <tr>
      <td>
        F
      </td>
      <td></td>
      <td></td>
      <td>
        \(x^2-16\)
      </td>
    </tr>
    <tr>
     <td>
        G
      </td>
      <td>
        \(3x-5\)
      </td>
      <td>
        \(3x-5\)
      </td>
      <td></td>
    </tr>
    <tr>
      <td>
        H
      </td>
      <td>
        \(3x-1\)
      </td>
      <td>
        \(x+2\)
      </td>
      <td></td>
    </tr>
    <tr>
      <td>
        I
      </td>
      <td>
        \(2x-3\)
      </td>
      <td></td>
      <td>
        \(4x^2-12x+9\)
      </td>
    </tr>
    <tr>
      <td>
        J
      </td>
      <td></td>
      <td></td>
      <td>
        \(x^2+6x-16\)
      </td>
    </tr>
    <tr>
      <td>
        K
      </td>
      <td>
        \(2x+3\)
      </td>
      <td>
        \(2x-3\)
      </td>
      <td></td>
    </tr>
    <tr>
      <td>
        L
      </td>
      <td></td>
      <td></td>
      <td>
        \(4x^2-12xy+9y^2-25\)
      </td>
    </tr>
  </tbody>
</table>
<br>
<h4>Student Response</h4>
<table class="os-raise-wideadjustedtable">
  <thead>

    <tr>
      <th scope="col"> Rectangle </th>
      <th scope="col"> Length (units) </th>
      <th scope="col"> Width (units) </th>
      <th scope="col"> Area (square units) </th>
    </tr>
    </thead>
      <tbody>
    <tr>
      <td>
        A
    </td>
      <td>
        \(x+3\)
      </td>
      <td>
        \(x-4\)
      </td>
      <td>
        \(x^2-x-12\)
      </td>
    </tr>
    <tr>
      <td>
        B
       </td>
      <td>
        \(3x+5\)
      </td>
      <td>
        \(3x-5\)
      </td>
      <td>
        \(9x^2-25\)
      </td>
    </tr>
    <tr>
      <td>
        C
      </td>
      <td>
        \(x+4\)
      </td>
      <td>
        \(x+4\)
      </td>
      <td>
        \(x^2+8x+16\)
      </td>
    </tr>
    <tr>
      <td>
        D
       </td>
      <td>
        \(x-2\)
      </td>
      <td>
        \(2x+1\)
      </td>
      <td>
        \(2x^2-3x-2\)
      </td>
    </tr>
    <tr>
      <td>
        E
       </td>
      <td>
        \(x-2\)
      </td>
      <td>
        \(x+6\)
      </td>
      <td>
        \(x^2+4x-12\)
      </td>
    </tr>
    <tr>
      <td>
        F
      </td>
      <td>
        \(x+4\)
      </td>
      <td>
        \(x-4\)
      </td>
      <td>
        \(x^2-16\)
      </td>
    </tr>
    <tr>
     <td>
        G
       </td>
      <td>
        \(3x-5\)
      </td>
      <td>
        \(3x-5\)
      </td>
      <td>
        \(9x^2-30x+25\)
      </td>
    </tr>
    <tr>
      <td>
        H
      </td>
      <td>
        \(3x-1\)
      </td>
      <td>
        \(x+2\)
      </td>
      <td>
        \(3x^2+5x-2\)
      </td>
    </tr>
    <tr>
      <td>
        I
       </td>
      <td>
        \(2x-3\)
      </td>
      <td>
        \(2x-3\)
      </td>
      <td>
        \(4x^2-12x+9\)
      </td>
    </tr>
    <tr>
      <td>
        J
      </td>
      <td>
        \(x-2\)
      </td>
      <td>
        \(x+8\)
      </td>
      <td>
        \(x^2+6x-16\)
      </td>
    </tr>
    <tr>
     <td>
        K
       </td>
      <td>
        \(2x+3\)
      </td>
      <td>
        \(2x-3\)
      </td>
      <td>
        \(4x^2-9\)
      </td>
    </tr>
    <tr>
      <td>
        L
       </td>
      <td>
        \(2x-3y-5\)
      </td>
      <td>
        \(2x-3y+5\)
      </td>
      <td>
        \(4x^2-12xy+9y^2-25\)
      </td>
    </tr>
  </tbody>
</table>
<br>
<h4>Activity Synthesis</h4>
<p>Invite students to share their answers and the methods they used to solve each rectangle.&nbsp;</p>
<p><strong>Use the following questions to lead a class discussion.</strong></p>
<ol>
  <li> How did you find the length when given the width and area? (Possible answer: multiply) </li>
  <li> How did you find the length and width given the area? (Possible answer: factor) </li>
  <li> Which rectangles represent perfect square trinomials? (Possible answers: C, G, I) </li>
  <li> Which rectangles represent the difference of squares? (Possible answers: B, F, K) </li>
  <li> Which rectangle(s) required grouping? (Possible answer: L) </li>
</ol>